Banca de DEFESA: JACKELLYNY DASSY DO NASCIMENTO CARVALHO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE: JACKELLYNY DASSY DO NASCIMENTO CARVALHO
DATA : 26/08/2024
HORA: 10:00
LOCAL: Sala 209
TÍTULO:

Control and Stabilization for the Nonlinear Schrödinger equation

PALAVRAS-CHAVES:

stabilization; critical exponent; profile decomposition; observability; microlocal measures; control; Strichartz estimates; defocusing case.

PÁGINAS: 150
RESUMO:

This thesis brings together some results related to the nonlinear $H^{1}$-critical Schrödinger equation in $\mathbb{R}^{3}$, in particular, an exact controllability result where, using Strichartz estimates, the controllability of the linear system (HUM method) and a perturbation argument, the controllability for the nonlinear system is achieved. Furthermore, for the aforementioned equation with a perturbation term, we prove exponential decay for some solutions which are bounded in energy space but small at a lower norm. This result is a consequence of a profile decomposition obtained for linear and nonlinear solutions combined with a propagation result that involves arguments from microlocal analysis, namely the defect measure theory. After showing that a
sequence of nonlinear solutions can be linearized under some conditions, we prove an observability estimate that concludes our stabilization result.

MEMBROS DA BANCA:
Externo à Instituição - DAVID DOS SANTOS FERREIRA
Externo à Instituição - ADÁN CORCHO
Externo à Instituição - FERNANDO ANDRES GALLEGO RESTREPO
Externo à Instituição - MARCELO MOREIRA CAVALCANTI
Presidente - 2257161 - ROBERTO DE ALMEIDA CAPISTRANO FILHO